The Distributive Property Law

In algebra and arithmetic, the distributive property law of numbers dictates their ability to be broken into smaller parts in order to perform complex multiplication with more ease. This is because the distributive property law allows mathematicians to calculate a large equation by multiplying each addend separately and then adding the products.

The distributive property helps with mental math and should be taught to children as a method to multiply larger numbers in their heads.

Take for instance needing to multiply 4 x 53. The distributive property law allows the equation to be distributed as (4 x 50) + (4 x 3) because the same number of "4s" will be added to the total when 4 is multiplied by both 50 and 3, which add up to 53. 

Basically, this allows for students to use easy-to-compute factors of multiplication in tandem with one another to quickly compute individual iterations of the final product. In the above equation, it's easy to multiply 4 x 50 and 4 x 3, so a student would be able to arrive at the simplified equation of (200) + (12) = 212.

Using the Distributive Property in Algebra

The distributive property is handy in getting rid of parenthetical in algebraic equations to help simplify the equation to solve for the missing number. Take for instance the equation a(b + c), which could be written as ab + ac because the distributive property dictates that the a outside the parenthetical must be multiplied by both the b and the c, which are separated by a plus sign.

To multiply in algebra, you also use the distributive property law, such is the case in the equation 3x(x + 4), which could be rewritten as 3x² + 12x according to the law.

Further, you can use the distributive property law to multiply and divide a polynomial by a monomial, expanding the product of the two.

Additionally, you can use the distributive property law to find the product of binomials, as shown here:

 (x + y)(x + 2y)
=(x + y)x + (x + y)(2y)
=x²+xy +2xy 2y²
=x² + 3xy +2y²

Another example:

2y(y-3)-3y(y+2)
=2y²-6y-3y²-6y
=-y²-12y

Practical Understanding of the Distributive Property Law

While it may not make much sense to students initially, understanding the core concept of the distributive property law is essential to being able to compute advanced math equations, especially those associated with algebra wherein some of the numbers are unknown.

Teachers should use these 8 early algebra worksheets and other tutorials to help students practice their understanding of how the distributive property law works, the first four of which do not involve exponents, which should make it easier for students to understand the basics of this important mathematical concept.

Another way to help students understand is by giving a practical example wherein you would need to apply the same distribution to an equation to make it uniformly increased. One such example would be expanding a recipe that is supposed to feed four people to be able to feed 40 people, which would require the baker to apply the distributive property law and multiply the quantity of each ingredient by the increase in the number of people the dish is meant to serve (10).